On Partial Sum of Tribonacci Numbers

الملخص EN

We study the sum s t ( k , r ) = ∑ i = 0 t T k i + r of k step apart Tribonacci numbers for any 1 ≤ r ≤ k .

We prove that s t ( k , r ) satisfies certain Tribonacci rule s t ( k , r ) = a k s t - 1 ( k , r ) + b k s t - 2 ( k , r ) + s t - 3 ( k , r ) + λ with integers a k , b k , c k , and λ .